Comment on "Direct Mapping of the Finite Temperature Phase Diagram of Strongly Correlated Quantum Models" by Q. Zhou, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. Lett. 103, 085701 (2009)

TL;DR

This paper critiques a previous claim that finite-temperature critical points in quantum models can be identified from density profile derivatives, showing that the original authors' method does not reliably achieve this under realistic conditions.

Contribution

It provides a critical analysis demonstrating that the proposed method for extracting critical densities from density profiles is not feasible in realistic experimental scenarios.

Findings

The method does not reliably identify critical points in realistic conditions.

Density profile derivatives are insufficiently precise for critical point determination.

The critique challenges the applicability of the original method in experimental settings.

Abstract

In their Letter, Zhou, Kato, Kawashima, and Trivedi claim that finite-temperature critical points of strongly correlated quantum models emulated by optical lattice experiments can generically be deduced from kinks in the derivative of the density profile of atoms in the trap with respect to the external potential, $\kappa = -dn(r)/dV(r)$. In this comment we demonstrate that the authors failed to achieve their goal: to show that under realistic experimental conditions critical densities $n_c(T,U)$ can be extracted from density profiles with controllable accuracy.